The \(S^{(a)}\)  observables are more prone to hadronic uncertainties. One can construct optimized observables with reduced uncertainties by proper combination of \(f_L\)  and \(S^{(a)}\)  observables. These observables have been proposed by several groups, see for e.g., [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. A frequently used form is the set of observables given in [6]}, [7]}. A generalized and extensive analysis of angular distribution formalism can be found in ref.[10]}. In this work, for \(B \rightarrow K^* \tau ^+ \tau ^-\)  decay, we consider the following set of optimized observables \(P^{(^{\prime })_i}\)  defined in ref. [6]}, [7]} and written in the basis of [13]}:
\(P_1 &=& \frac{S_3}{2 S_2^s}, \,\, P_2=\frac{S_6^s}{8 S_2^s}, \,\, P_3=\frac{S_{9}}{4 S_2^s}\,,\nonumber \\P^{\prime }_4 &=& \frac{S_4}{2\sqrt{-S_2^s S_2^c}}, \,\,P^{\prime }_5 = \frac{S_5}{2\sqrt{-S_2^s S_2^c}}\,,\nonumber \\P^{\prime }_6 &=& \frac{S_7}{2\sqrt{-S_2^s S_2^c}}, \,\, P^{\prime }_8 = \frac{S_8}{2\sqrt{-S_2^s S_2^c}}\,.\) 
